Graph Layout Problems Parameterized by Vertex Cover

Fellows, Michael R.; Lokshtanov, Daniel; Misra, Neeldhara; Rosamond, Frances A.; Saurabh, Saket

doi:10.1007/978-3-540-92182-0_28

Cited by 122 publications

(84 citation statements)

References 23 publications

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“…This is, of course, just the size of a minimal vertex cover in G and is a parameter that has been much studied (see for instance [7]). Indeed, it is also quite straightforward to see that GI is FPT when parameterized by vertex cover number.…”

Section: Introductionmentioning

confidence: 99%

Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree

Bulian

Dawar

2015

Algorithmica

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A commonly studied means of parameterizing graph problems is the deletion distance from triviality (Guo et al., Parameterized and exact computation, Springer, Berlin, pp. 162-173, 2004), which counts vertices that need to be deleted from a graph to place it in some class for which efficient algorithms are known. In the context of graph isomorphism, we define triviality to mean a graph with maximum degree bounded by a constant, as such graph classes admit polynomial-time isomorphism tests. We generalise deletion distance to a measure we call elimination distance to triviality, based on elimination trees or tree-depth decompositions. We establish that graph canonisation, and thus graph isomorphism, is FPT when parameterized by elimination distance to bounded degree, extending results of Bouland et al. (Parameterized and exact computation, Springer, Berlin, pp. 218-230, 2012).

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Section: Introductionmentioning

confidence: 99%

Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree

Bulian

Dawar

2015

Algorithmica

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“…This fact is used to obtain Fpt algorithms for many hard problems, e.g., see [9]. The same phenomenon leads to ParaPspace algorithms for Petri net coverability and boundedness.…”

Section: Vertex Cover For Petri Netsmentioning

confidence: 94%

Small Vertex Cover makes Petri Net Coverability and Boundedness Easier

Praveen

2012

Algorithmica

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Abstract. The coverability and boundedness problems for Petri nets are known to be Expspacecomplete. Given a Petri net, we associate a graph with it. With the vertex cover number k of this graph and the maximum arc weight W as parameters, we show that coverability and boundedness are in ParaPspace. This means that these problems can be solved in space O (ef (k, W )poly(n)), where ef (k, W ) is some exponential function and poly(n) is some polynomial in the size of the input. We then extend the ParaPspace result to model checking a logic that can express some generalizations of coverability and boundedness.

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“…This is the first non-trivial exact exponential time algorithm for CUTWIDTH on a graph class where the problem is NP-complete. Furthermore, our algorithm improves considerably over the previous best algorithm for CUTWIDTH parameterized by vertex cover [15], whose running time is O(2 2 O(k) n O (1) ) (however, it was not the focus of [15] to optimize the running time dependence on k).…”

Section: Introductionmentioning

confidence: 90%

On Cutwidth Parameterized by Vertex Cover

et al. 2012

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We study the CUTWIDTH problem, where the input is a graph G, and the objective is find a linear layout of the vertices that minimizes the maximum number of edges intersected by any vertical line inserted between two consecutive vertices. We give an algorithm for CUTWIDTH with running time O(2 k n O(1) ). Here k is the size of a minimum vertex cover of the input graph G, and n is the number of vertices in G. Our algorithm gives an O(2 n/2 n O(1) ) time algorithm for CUTWIDTH on bipartite graphs as a corollary. This is the first non-trivial exact exponential time algorithm for CUTWIDTH on a graph class where the problem remains NP-complete. Additionally, we show that CUTWIDTH parameterized by the size of the minimum vertex cover of the input graph does not admit a polynomial kernel unless NP ⊆ coNP/poly. Our ker- (ICALP, Springer, Berlin, 2011; SWAT, Springer, Berlin, 2012) that both TREEWIDTH and PATHWIDTH parameterized by vertex cover do admit polynomial kernels.

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Graph Layout Problems Parameterized by Vertex Cover

Cited by 122 publications

References 23 publications

Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree

Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree

Small Vertex Cover makes Petri Net Coverability and Boundedness Easier

On Cutwidth Parameterized by Vertex Cover

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